Nonresonant Three-body Decays of D and B Mesons

Nonresonant three-body decays of D and B mesons are studied. It is pointed out that if heavy meson chiral perturbation theory (HMChPT) is applied to the heavy-light strong and weak vertices and assumed to be valid over the whole kinematic region, then the predicted decay rates for nonresonant charmless 3-body B decays will be too large and especially B− → π−K+K− greatly exceeds the current experimental limit. This can be understood as chiral symmetry has been applied there twice beyond its region of validity. If HMChPT is applied only to the strong vertex and the weak transition is accounted for by the form factors, the dominant B∗ pole contribution to the tree-dominated direct three-body B decays will become small and the branching ratio will be of order 10−6. The decay modes B− → (K−h+h−)NR and B → (Kh+h−)NR for h = π,K are penguin dominated. We apply HMChPT in two different cases to study the direct 3-body D decays and compare the results with experiment. The preliminary FOCUS measurement of the direct decay D+ s → (π+π+π−)NR may provide the first indication of the importance of final-state interactions for the weak annihilation process in nonresonant D decays. Theoretical uncertainties are discussed.